In 1941, Joe DiMaggio got at least one hit in 56 consecutive games, still the record for the longest hitting streak in Major League Baseball. Let’s try to estimate the probability of someone like DiMaggio achieving the success he did. That year, he had a batting average of 0.357. We will assume that for each at bat, the probability he would get a hit stays constant at 0.357. He had slightly fewer than four at bats per game. To simplify things, we will assume he bats exactly 4 times per game. 

a. We first need to find the probability he would get at least one hit in a game. 

i. What is the probability he does not get a hit at one at bat? 

ii. What is the probability he does not get any hits (with four at bats) in a single game? 

iii. What is the probability he gets at least one hit in a single game? 

b. Now what is the probability he gets at least one hit in 56 consecutive games? 

c. In 1941, the regular baseball season consisted of 154 games. Is the probability you found in part (b) a good estimate for the probability he would have gotten at least one hit in 56 consecutive games sometime during the season, or should that estimate be larger or smaller?